Mensa IQ Test Mensa IQ Cube, Dice and Paper Folding 1 — Questions and Answers
Question 1: A standard die has opposite faces summing to 7. If the face showing 3 is on top and the face showing 1 faces you, which number is on the bottom?
- 4 (Correct answer)
- 6
- 2
- 5
Correct answer: 4
Opposite faces on a standard die sum to 7, so 3 is opposite 4; with 3 on top, 4 is on the bottom.
Question 2: A square piece of paper is folded in half vertically, then folded in half horizontally. A circular hole is punched through all layers at the center of the folded square. When fully unfolded, how many holes appear?
- 4 (Correct answer)
- 1
- 2
- 8
Correct answer: 4
Each fold doubles the layers, so two folds produce 4 layers; one punch creates 4 holes when unfolded.
Question 3: A cube net (cross-shaped) has a star on the center square, a circle on the square directly above it, and a triangle on the square directly below it. When folded, what shape is on the face opposite the star?
- Triangle
- Circle (Correct answer)
- Neither — star has no opposite
- Square
Correct answer: Circle
In a standard cross-shaped net, the top and bottom extensions fold to become opposite faces, so the circle (above the star) ends up opposite the triangle (below), and the star's opposite is determined by the remaining face — but in this cross layout the square directly above folds to be opposite the square directly below, making the circle opposite the triangle; the star's opposite is the one square to the side not mentioned, but given only these three, circle is on the face opposite triangle, and the face above the center folds to face the center, so the circle faces the star's opposite direction — the circle is opposite the star.
Question 4: Three dice are stacked vertically. The top die shows 5 on top. The middle die shows 2 on its visible front face. The bottom die shows 1 on its right side. What is the sum of all hidden face values touching between the top and middle dice?
- 7 (Correct answer)
- 5
- 9
- 12
Correct answer: 7
The two touching faces between adjacent dice must each be part of an opposite-face pair; since opposite faces sum to 7, the two touching faces together sum to 7.
Question 5: A rectangular piece of paper is folded once diagonally so two corners meet. A triangular notch is cut from the folded edge at the midpoint. When unfolded, what shape is the cutout?
- Diamond (rhombus) (Correct answer)
- Triangle
- Square
- Circle
Correct answer: Diamond (rhombus)
Cutting a triangle from a single folded edge creates a mirror image on both halves, producing a diamond/rhombus shape when unfolded.
Question 6: A die is placed on a table with 6 on top and 2 facing north. It is rolled one step to the east (tilted 90° eastward). What number is now on top?
- 3
- 4 (Correct answer)
- 1
- 5
Correct answer: 4
Rolling east tilts the die 90°: the eastern face (which was 3, since 4 is east on a standard die) comes to the top, so 4 is now on top.
Question 7: How many unit cubes make up a 3×3×3 cube with the inner core removed (only the outer shell remains)?
- 26 (Correct answer)
- 27
- 18
- 24
Correct answer: 26
A 3×3×3 cube has 27 unit cubes total; removing the 1 center cube that is not visible from any face leaves 26.
Mensa IQ Test Mensa IQ Cube, Dice and Paper Folding 1
A standard die has opposite faces summing to 7.
If the face showing 3 is on top and the face showing 1 faces you, which number is on the bottom?